Center of mass acceleration in coupled nanowaveguides due to transverse optical beating force

Eigenmode optical forces arising in symmetrically coupled waveguides have opposite sign on opposite waveguides and thus can deform the waveguides by changing their relative separation, but cannot change any other degree of freedom on their own. It would be extremely desirable to have a way to act on the center of mass of such a system. In this work we show that it is possible to do so by injecting a superposition of eigenmodes that are degenerate in frequency and have opposite parity along the desired direction, resulting in beating forces that have the same sign on opposite waveguides and therefore act on the center of mass. We have used both the Maxwell Stress Tensor formalism and the induced dipole force equation to numerically calculate this transverse beating force and have found its magnitude to be comparable to the eigenmode forces. We also show that the longitudinal variation caused by the spatial beating pattern on the time-averaged quantities used in the calculations must be taken into account in order to properly employ the divergence theorem and obtain the correct magnitudes. We then propose a heuristic model that shows good quantitative agreement with the numerical results and may be used as a prototyping tool for accurate and fast computation without relying on expensive numerical computation.